Linear Matrix Inequality Approach to Stochastic Stabilization of Networked Control System with Markovian Jumping Parameters

Abstract

This paper is concerned with the stochastic stabilization problem for a class of networked control system (NCS) with destabilizing transmission factors. By introducing the effective sampling instant to model random time delays and successive packet dropouts as two independent Markov chains, NCS is modeled as a discrete-time Markovian jump linear system with mixed integrated Markovian jumping parameters. In this way, a novel framework to analyze the stochastic stabilization problem of NCS is provided. The necessary and sufficient conditions for the stochastic stabilization of the NCS are obtained by the Lyapunov method and the state-feedback controller gain that depends on the delay modes is obtained in terms of the linear matrix inequalities (LMIs) formulation via the Schur complement theory. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Keywords

Recommended by Associate Editor Yingmin Jia under the direction of Editor PooGyeon Park. This work was supported by National Natural Science Foundation of China under grant 51707158, Natural Science Foundation Research Project of Shaanxi Province of China under grant 2016JM6021 and 2018JQ6006, and China Scholarship Council under grant 201808610075.

Yanpeng Wu received his Ph.D. in Control Science and Engineering from Northwestern Polytechnical University, Xi’an, China in 2015. He is currently a teacher at School of Building Services Science and Engineering, Xi’an University of Architecture and Technology. His current research interests include advanced control theory and application, networked control systems and fault diagnosis and control.

Ying Wu received her Ph.D. in Control Science and Engineering from Northwestern Polytechnical University, Xi’an, China in 2014. She is currently a teacher at School of Computer Science, Xi’an Shiyou University. Her current research interests include networked control systems and Microgrid control and optimization.

A. C. Probst and E. M. Mario, “Compensating random time delays in a feedback networked control system with a Kalman filter,” Journal of Dynamic Systems Measurement and Control–Transactions of the Asme, vol. 133, no. 2, pp. 1–5, January 2011.Google Scholar